分类算法KNN(K Nearest Neighbor)
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示例：《电影类型分类》
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获取数据来源
| 电影名称 | 打斗次数 | 接吻次数 | 电影类型 |
|---|---|---|---|
| California Man | 3 | 104 | Romance |
| He's Not Really into Dudes | 8 | 95 | Romance |
| Beautiful Woman | 1 | 81 | Romance |
| Kevin Longblade | 111 | 15 | Action |
| Roob Slayer 3000 | 99 | 2 | Action |
| Amped II | 88 | 10 | Action |
| Unknown | 18 | 90 | unknown |
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数据显示：肉眼判断电影类型unknown是什么
from matplotlib import pyplot as plt # 用来正常显示中文标签 plt.rcParams["font.sans-serif"] = ["SimHei"] # 电影名称 names = ["California Man", "He's Not Really into Dudes", "Beautiful Woman", "Kevin Longblade", "Robo Slayer 3000", "Amped II", "Unknown"] # 类型标签 labels = ["Romance", "Romance", "Romance", "Action", "Action", "Action", "Unknown"] colors = ["darkblue", "red", "green"] colorDict = {label: color for (label, color) in zip(set(labels), colors)} print(colorDict) # 打斗次数，接吻次数 X = [3, 8, 1, 111, 99, 88, 18] Y = [104, 95, 81, 15, 2, 10, 88] plt.title("通过打斗次数和接吻次数判断电影类型", fontsize=18) plt.xlabel("电影中打斗镜头出现的次数", fontsize=16) plt.ylabel("电影中接吻镜头出现的次数", fontsize=16) # 绘制数据 for i in range(len(X)): # 散点图绘制 plt.scatter(X[i], Y[i], color=colorDict[labels[i]]) # 每个点增加描述信息 for i in range(0, 7): plt.text(X[i]+2, Y[i]-1, names[i], fontsize=14) plt.show()
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问题分析：根据已知信息分析电影类型unknown是什么
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核心思想：未标记样本的类别由距离其最近的K个邻居的类别决定
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距离度量：一般距离计算使用欧式距离（用勾股定理计算距离），也可以采用曼哈顿距离（水平上和垂直上的距离之和）、余弦值和相似度（这是距离的另一种表达方式）。相比于上述距离，马氏距离更为精确，因为它能考虑很多因素，比如单位，由于在求协方差矩阵逆矩阵的过程中，可能不存在，而且若碰见3维及3维以上，求解过程中极其复杂，故可不使用马氏距离
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知识扩展
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马氏距离概念：表示数据的协方差距离
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方差：数据集中各个点到均值点的距离的平方的平均值
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标准差：方差的开方
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协方差cov(x, y)：E表示均值，D表示方差，x，y表示不同的数据集，xy表示数据集元素对应乘积组成数据集
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cov(x, y) = E(xy) - E(x)*E(y)
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cov(x, x) = D(x)
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cov(x1+x2, y) = cov(x1, y) + cov(x2, y)
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cov(ax, by) = abcov(x, y)
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协方差矩阵：根据维度组成的矩阵，假设有三个维度，a，b，c
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∑ij = [cov(a, a) cov(a, b) cov(a, c) cov(b, a) cov(b,b) cov(b, c) cov(c, a) cov(c, b) cov(c, c)]
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算法实现：欧氏距离
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编码实现
# 自定义实现 mytest1.py import numpy as np # 创建数据集 def createDataSet(): features = np.array([[3, 104], [8, 95], [1, 81], [111, 15], [99, 2], [88, 10]]) labels = ["Romance", "Romance", "Romance", "Action", "Action", "Action"] return features, labels def knnClassify(testFeature, trainingSet, labels, k): """ KNN算法实现，采用欧式距离 :param testFeature: 测试数据集，ndarray类型，一维数组 :param trainingSet: 训练数据集，ndarray类型，二维数组 :param labels: 训练集对应标签，ndarray类型，一维数组 :param k: k值，int类型 :return: 预测结果，类型与标签中元素一致 """ dataSetsize = trainingSet.shape[0] """ 构建一个由dataSet[i] - testFeature的新的数据集diffMat diffMat中的每个元素都是dataSet中每个特征与testFeature的差值（欧式距离中差） """ testFeatureArray = np.tile(testFeature, (dataSetsize, 1)) diffMat = testFeatureArray - trainingSet # 对每个差值求平方 sqDiffMat = diffMat ** 2 # 计算dataSet中每个属性与testFeature的差的平方的和 sqDistances = sqDiffMat.sum(axis=1) # 计算每个feature与testFeature之间的欧式距离 distances = sqDistances ** 0.5 """ 排序，按照从小到大的顺序记录distances中各个数据的位置 如distance = [5, 9, 0, 2] 则sortedStance = [2, 3, 0, 1] """ sortedDistances = distances.argsort() # 选择距离最小的k个点 classCount = {} for i in range(k): voteiLabel = labels[list(sortedDistances).index(i)] classCount[voteiLabel] = classCount.get(voteiLabel, 0) + 1 # 对k个结果进行统计、排序，选取最终结果，将字典按照value值从大到小排序 sortedclassCount = sorted(classCount.items(), key=lambda x: x[1], reverse=True) return sortedclassCount[0][0] testFeature = np.array([100, 200]) features, labels = createDataSet() res = knnClassify(testFeature, features, labels, 3) print(res) # 使用python包实现 mytest2.py from sklearn.neighbors import KNeighborsClassifier from .mytest1 import createDataSet features, labels = createDataSet() k = 5 clf = KNeighborsClassifier(k_neighbors=k) clf.fit(features, labels) # 样本值 my_sample = [[18, 90]] res = clf.predict(my_sample) print(res)
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示例：《交友网站匹配效果预测》
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数据来源：略
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数据显示
import pandas as pd import numpy as np from matplotlib import pyplot as plt from mpl_toolkits.mplot3d import Axes3D # 数据加载 def loadDatingData(file): datingData = pd.read_table(file, header=None) datingData.columns = ["FlightDistance", "PlaytimePreweek", "IcecreamCostPreweek", "label"] datingTrainData = np.array(datingData[["FlightDistance", "PlaytimePreweek", "IcecreamCostPreweek"]]) datingTrainLabel = np.array(datingData["label"]) return datingData, datingTrainData, datingTrainLabel # 3D图显示数据 def dataView3D(datingTrainData, datingTrainLabel): plt.figure(1, figsize=(8, 3)) plt.subplot(111, projection="3d") plt.scatter(np.array([datingTrainData[x][0] for x in range(len(datingTrainLabel)) if datingTrainLabel[x] == "smallDoses"]), np.array([datingTrainData[x][1] for x in range(len(datingTrainLabel)) if datingTrainLabel[x] == "smallDoses"]), np.array([datingTrainData[x][2] for x in range(len(datingTrainLabel)) if datingTrainLabel[x] == "smallDoses"]), c="red") plt.scatter(np.array([datingTrainData[x][0] for x in range(len(datingTrainLabel)) if datingTrainLabel[x] == "didntLike"]), np.array([datingTrainData[x][1] for x in range(len(datingTrainLabel)) if datingTrainLabel[x] == "didntLike"]), np.array([datingTrainData[x][2] for x in range(len(datingTrainLabel)) if datingTrainLabel[x] == "didntLike"]), c="green") plt.scatter(np.array([datingTrainData[x][0] for x in range(len(datingTrainLabel)) if datingTrainLabel[x] == "largeDoses"]), np.array([datingTrainData[x][1] for x in range(len(datingTrainLabel)) if datingTrainLabel[x] == "largeDoses"]), np.array([datingTrainData[x][2] for x in range(len(datingTrainLabel)) if datingTrainLabel[x] == "largeDoses"]), c="blue") plt.xlabel("飞行里程数", fontsize=16) plt.ylabel("视频游戏耗时百分比", fontsize=16) plt.clabel("冰淇凌消耗", fontsize=16) plt.show() datingData, datingTrainData, datingTrainLabel = loadDatingData(FILEPATH1) datingView3D(datingTrainData, datingTrainLabel)
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问题分析：抽取数据集的前10%在数据集的后90%进行测试
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编码实现
# 自定义方法实现 import pandas as pd import numpy as np # 数据加载 def loadDatingData(file): datingData = pd.read_table(file, header=None) datingData.columns = ["FlightDistance", "PlaytimePreweek", "IcecreamCostPreweek", "label"] datingTrainData = np.array(datingData[["FlightDistance", "PlaytimePreweek", "IcecreamCostPreweek"]]) datingTrainLabel = np.array(datingData["label"]) return datingData, datingTrainData, datingTrainLabel # 数据归一化 def autoNorm(datingTrainData): # 获取数据集每一列的最值 minValues, maxValues = datingTrainData.min(0), datingTrainData.max(0) diffValues = maxValues - minValues # 定义形状和datingTrainData相似的最小值矩阵和差值矩阵 m = datingTrainData.shape(0) minValuesData = np.tile(minValues, (m, 1)) diffValuesData = np.tile(diffValues, (m, 1)) normValuesData = (datingTrainData-minValuesData)/diffValuesData return normValuesData # 核心算法实现 def KNNClassifier(testData, trainData, trainLabel, k): m = trainData.shape(0) testDataArray = np.tile(testData, (m, 1)) diffDataArray = (testDataArray - trainData) ** 2 sumDataArray = diffDataArray.sum(axis=1) ** 0.5 # 对结果进行排序 sumDataSortedArray = sumDataArray.argsort() classCount = {} for i in range(k): labelName = trainLabel[list(sumDataSortedArray).index(i)] classCount[labelName] = classCount.get(labelName, 0)+1 classCount = sorted(classCount.items(), key=lambda x: x[1], reversed=True) return classCount[0][0] # 数据测试 def datingTest(file): datingData, datingTrainData, datingTrainLabel = loadDatingData(file) normValuesData = autoNorm(datingTrainData) errorCount = 0 ratio = 0.10 total = datingTrainData.shape(0) numberTest = int(total * ratio) for i in range(numberTest): res = KNNClassifier(normValuesData[i], normValuesData[numberTest:m], datingTrainLabel, 5) if res != datingTrainLabel[i]: errorCount += 1 print("The total error rate is : {} ".format(error/float(numberTest))) if __name__ == "__main__": FILEPATH = "./datingTestSet1.txt" datingTest(FILEPATH) # python 第三方包实现 import pandas as pd import numpy as np from sklearn.neighbors import KNeighborsClassifier if __name__ == "__main__": FILEPATH = "./datingTestSet1.txt" datingData, datingTrainData, datingTrainLabel = loadDatingData(FILEPATH) normValuesData = autoNorm(datingTrainData) errorCount = 0 ratio = 0.10 total = normValuesData.shape[0] numberTest = int(total * ratio) k = 5 clf = KNeighborsClassifier(n_neighbors=k) clf.fit(normValuesData[numberTest:total], datingTrainLabel[numberTest:total]) for i in range(numberTest): res = clf.predict(normValuesData[i].reshape(1, -1)) if res != datingTrainLabel[i]: errorCount += 1 print("The total error rate is : {} ".format(errorCount/float(numberTest)))